Treatment-Response Models for Counterfactual Reasoning with Continuous-time, Continuous-valued Interventions

TL;DR

This paper introduces a novel approach for estimating treatment effects in observational data with continuous, time-varying interventions, using dynamical systems and Gaussian Processes to improve accuracy in complex, irregularly measured outcomes.

Contribution

The paper presents a new method combining linear time-invariant dynamical systems with multi-output Gaussian Processes for modeling continuous-time, continuous-valued treatment responses in multivariate data.

Findings

Significant accuracy improvements over existing models on simulated data.

Effective modeling of complex correlation structures across multiple signals.

Robust performance on challenging clinical datasets.

Abstract

Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time. Further, the outcome variable may not be measured at a regular frequency. Our proposed solution represents the treatment response curves using linear time-invariant dynamical systems---this provides a flexible means for modeling response over time to highly variable dose curves. Moreover, for multivariate data, the proposed method: uncovers shared structure in treatment response and the baseline across multiple markers; and, flexibly models challenging correlation structure both across and within signals over time. For this, we build upon the framework of multiple-output Gaussian Processes. On simulated and a challenging clinical dataset, we show significant gains in accuracy over state-of-the-art models.